Problem: Solve for $x$ and $y$ using elimination. ${-3x-5y = -77}$ ${3x-4y = -13}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-9y = -90$ $\dfrac{-9y}{{-9}} = \dfrac{-90}{{-9}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x-5y = -77}\thinspace$ to find $x$ ${-3x - 5}{(10)}{= -77}$ $-3x-50 = -77$ $-3x-50{+50} = -77{+50}$ $-3x = -27$ $\dfrac{-3x}{{-3}} = \dfrac{-27}{{-3}}$ ${x = 9}$ You can also plug ${y = 10}$ into $\thinspace {3x-4y = -13}\thinspace$ and get the same answer for $x$ : ${3x - 4}{(10)}{= -13}$ ${x = 9}$